Factoring Patterns
5-8Factoring Pattern for x² + bx + c, c negative
Overview
Numbers have opposite signs; the larger absolute value takes the sign of b.
Key ideas
- Find pair whose product is c (negative).
- Whose sum is b.
- One factor positive, one negative.
Worked examples
Example 1
Problem. Factor x^2 + 2x − 15.
Solution. (x + 5)(x − 3)
Example 2
Problem. Factor x^2 − 4x − 12.
Solution. (x − 6)(x + 2)
Practice
Try each one. Click Show answer when ready.
- 1.
Factor x^2 − 3x − 10.
- 2.
Factor x^2 + 5x − 14.
- 3.
Factor x^2 − x − 20.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Factor: x² + 5x − 24.
- 2.
Factor: x² − 2x − 35.